Frontier Airlines' new policy that tacks on a fee for passengers who book tickets on third-party websites went into effect Tuesday, yet several of the online travel agencies have found ways to circumvent the penalty for its customers.

Priceline.com announced Tuesday that its customers can still book Frontier tickets that include a free carry-on bag despite the Denver-based carrier's recent changes.

Frontier announced at the beginning of the summer that it would start charging customers for a carry-on bag if they don't book directly through its FlyFrontier.com website. However, Priceline says that its customers will not be subject to the penalty if they book an Economy fare ticket or higher.

The moral of the story is to read the fine print.

Here is how it works:

The airline offers three fare brackets on its website - Economy, Classic and Classic Plus. All of these tickets still offer a free carry-on bag.

Things get murky -- and possibly intentionally so -- once you start dabbling in third-party travel websites, such as Orbitz, KAYAK and Priceline.

Frontier's often unknown fourth fare bracket -- Basic -- is only available on the third-party sites and are the only tickets that no longer comes with a free carry-on bag.

"We offer all of our distributors all four fares brackets," said Kate O'Malley, Frontier's spokeswoman, who couldn't speak to the methodology of the third-party sites for findings its customers the cheapest fares. But, she said, "The effort is still to get customers to book on FlyFrontier.com."

Priceline also claims that customers using the website's trademark "Name Your Own Price" airline tickets will also get a free carry-on bag if they receive a Frontier itinerary, which implies that it has axed the Basic fare from its structure. The company could not be reached for comment.

After attempting to go through the booking process on a number of sites, it appears that your best bet for locking in a free carry-on is to either read the itinerary's fine print to make sure it says "Economy" on your ticket or do as the airline wishes and book through its website.